Low SNR Capacity of Fading Channels – MIMO and multipath

Discrete-time noncoherent Rayleigh fading multiple-input multiple-output (MIMO) channels are considered, with no channel state information at either the transmitter or the receiver. The fading is assumed to be correlated in time and independent from antenna to antenna. Peak and average transmit power constraints are imposed, either on the sum over antennas, or on each individual antenna. In both cases, an upper bound and an asymptotic lower bound, as the signal-to-noise ratio approaches zero, on the channel capacity are presented. The capacity asymptote is identified under the sum power constraints. For the individual power constraints, bounds on the capacity asymptote are presented and shown to be tight under certain conditions. These results are applied to a SISO channel with multipath fading. For such a channel, the multiple transmission paths play the role of multiple transmit antennas. Upper and lower bounds on the low SNR capacity asymptote are presented and shown to coincide under certain conditions.